Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}8x-2y &= 8 \\ -8x+9y &= 6\end{align*}$
Solution: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $7y = 14$ Divide both sides by $7$ and reduce as necessary. $y = 2$ Substitute $2$ for $y$ in the top equation. $8x-2( 2) = 8$ $8x-4 = 8$ $8x = 12$ $x = \dfrac{3}{2}$ The solution is $\enspace x = \dfrac{3}{2}, \enspace y = 2$.